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A PREDICTION OF THE DOWNSTREAM RESPONSE OF POPLAR CREEK, CALIFORNIA

TO THE DUTCH GULCH DAM

Gary Parker ft.ssociate Professor, St. Anthony Falls Hydraulic

Laboratory: Minneapolis, Minnesota, U£S.A.

INTRODUCTION

The present paper represents my effort to predict the likely hydrau]fc and morphologic response of Poplar Creek downstream of t.he proposed Dutch Gulch Dam to the extent that is allowed by the voluminous but incompl~te data provided to me by the workshop org~nizers.

1f the reader considers the use of the ffrst person pretentious,. allow me to remaN that a prediction of thfs sort is by nature a highly personal one. "Intelligent" guessing is required in step after step in order to f i 11 the gaps in even the most comprehensive data set. By using the first person, I hope to elucidate the thought processes of the subjective decisions necessary for this prediction.

The prediction proceeds in 11 steps outlined below.

1. Delineation of the reaches.

2. Geometric data.

·~ 3. Bed material.

4. Geometric data synthesized from hydro'Joglc considerations.

5. Natural and project flow duration curves.

6. Water and 91"'avel routing for natural conditions.

7. Short term water and gravel routing for project conditions ignoring tributary degradation.

B. The short term effect of tributary degr~dation. 9. Long term changes in channel geometry.

10. Meandering and the pool-and-riffle structure.

11. Summary of predictions for "Poplar" Creek and fts tributaries.

128

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DELINEATION OF THE REACHES.

I considered the four reaches schematized in Figure 1. They a

Reach 1. Poplar Creek from Dutch Gulch to just upstream of Dry Creek.

Reach 2. Poplar Creek from just upstream of Dry Creek to elevation 430 feet.

Reach 3. Little Dry Creek from the confluence with Poplar Creek to elevation 540 feet.

Reach 4. Dry Creek from the confluence with Poplar Creek to elevation 560 feet. ·

The elevations refer to stream elevations on the 1965 U.S. Geological Survey 1:24000 map of the Hooker, California quadrangle. The 430-foot point is about 2 km upstream of the confluence with the South Fork.

In fact, Dry Craek and Little Dry Creek join Poplar Creek at po·Ints so close together that for the purposes of the analysis I decided to proceed under the assumption that the confluences coincide at a point corresponding to the average of the two.

The reason for the above choice of reaches is as follows. Having been given practi ca 1ly no information about the South Fork or any projects on it, I assumed that it remains unchanged. To be on the safe side, Reach 2 was chosen so as not to include it. There are no tributaries of any consequence in Reach 1, which would be the one immediately below the dam. Reach 2 contains two tributaries of con­sequence; namely, Reaches 3 and 4 at its upstream end.

Both water and grave 1 can be routed through the system of four reaches for natural and project conditions. Down-channel reach lengths are given in Table 1.

Table 1. Down-channel reach lengths.

REACH LENGTH (km)

1 8.26 2 6.23 3 6.13 4 4.57

MEASURED GEOMETRIC DATA ~$

f} I determined overa 11 dow·n-channe 1 s 1 opes S for the four reaches by considering the elevation drop over lengths chosen to contain, but be

ll ' 11

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Reach I Reach 2 ~--------~------~----------~------~~-~ (Poplar Creek) ,/

/

~~~~ ""'" ~0 / ~~

d" ~ e:,O

Figure I. Definition of reaches.

130

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a little longer than, each reach. The values were read from the supplied 1:24000 topographical maps. The values are S = 0.00180, 0.00186, 0.00390, and 0.00569 for Reaches 1 to 4, respectively.

Data on channe 1 cross-section a 1 geometry were supp 1 i ed only for Reach 2. I determined average bankfull water surface width Bb and

cross-sectionally averaged depth Hb for the cross sections labeled 57

to 65. The values are Bb =119m and Hb = 2.25 m.

Values for Bb and Hb for the other three reaches were

synthesized in the fashions outlined subsequently.

BED MATERIAL

The bed material data on Poplar Creek dated August 1978 were used to obtain a representative grain size distribution. Of the seventeen samples listed therein, I could not locate samples ZF-78-3, -4, or -5 on the attached map. Of the remaining fourteen samples, seven were taken at the water's edge, and seven were from overbank. Each sample is a bulk sample of at least two sacks.

Most grave 1-bed streams have a surface pavement which is two or three times coarser than the underlying subpavement. A 1 arge bulk sample taken in the submerged channel typically contains mostly sub­pavement, but cons i derab 1 e amounts of pavement. However, Parker and Klingeman (1980) have argued that large bulk samples taken on exposed bars near the water's edge provide a reasonable approximation of the subpavement of the channel proper. I used this assumption in analyzing the seven data sets from the water's edge.

The sample 2F-78-1 proved to be markedly finer than the six others, so I rejected it as being uncharacteristic. The other six samples were averaged to yi e 1 d a "typi ca 111 expected subpavement distribution for Poplar Creek, including Reaches 1 and 2. The average size ciistribution is given in Figure 2. Subpavement o50 and o90 are seen to be about

20 and 106 mm, respectively; fines (sand) cont-ent is about twenty percent.

None of the seven overbank samples appeared to be anomalous. I averaged them to obt~in a "typical" overbank sediment distribution with o50 = 25 mm, o90 = 130 mm, and eighteen percent fines content. The

average overbank size distribution ~s also known in Figure 2.

Severa 1 re 1 evant observations can be made here. The va 1 ues of subpavement o50 , o90 $) and fines content for Poplar Creek are very

similar to the values for four gravel-bed streams on which extensive gravel bedload measurements have been made; name1y Oak Creek, Oregon; Elbow River, Alberta; Vedder River, British Columbia; and Snake River,

131

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10 Grain Size, mm

Figure 2. Grain-size distributions.

132

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Idaho. Parker, Klfngeinan, and Mclean (1980) have used these data to determine a bedload relation for field gravel-bed streams. Thus, I feel at least partially justified in applying th~ relation to Poplar Creek .

Also, the overbank size distribution is about the same as that of the subpavement. This suggests that vegetation and cohesive material do not act as significant controls on channel width. Recently I (Parker, 1980) determined several sets of empirical relations for bankfull hydraulic geometry. One set, using 21 reaches mostly from A 1 berta and British Co 1 umbi a, Canada corresponds to grave 1-bed streams with gLavelly banks and little cohesion, in regions that are semiarid or only modl!i-atii'J.Y~liUniicf:--theWfdtJl-·an·d depth relations are shown in Figures 3a and 3b; they and the corresponding correlation coefficients are:

sb = 5.86 Qb0.441 r2 = 0.931 (1a)

Hb = 0.188 Qb0.416 r2 = 0.860 (lb)

where Qb is bankfull discharge. The units are S.I. I assumed these relations to hold with a reasonable degree of accuracy for Poplai" Creek and its tributaries.

A third point concerns roughness height k in the Keulegan resistance equation; where V is flow velocity and g is gravitational acceleration,

__y_ = 2.5tn (11~) /gHS (2)

Pa·· .. ker and Peterson (1980) have followed the lead of several other investigators and have provided justification for the approximation

at flood stages (the only stages which normally move gravel in gravel­bed streams). The subscript p refers to pavement.

Pavement size distributions for Poplar Creek were not available. However, experience suggests to me that a bulk surficial median pavement size should be two to three times coarser than the subpavement o

50; i.e.

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a British Single Channel (Set I) o Alberta Single Channel (Set 2) o Sunwopta Attabranches (Sot 3) • Laboratory Anabranchts lSet 4)

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Fiaure Ja. Widtb_relat1ons.

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I Fiaure lb. Depth relations.

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in this case DpSO = 50 m~. ~,owever,,. t~e sa~~e e~perience .suggest~ that

pavement Dpgo and subpavement o90 ·'are. fn mos~ cases not much

different. With this in mind, I estimated k = 0.212 m. '

\ ~ .. :f.

Ava i 1 ab 1 e d~t~ for Reaches 3 and 4 were at best sketchy. The only bed samples pertc\ining to them \'Jere hole number 5 for Little Dry Creek, with a o50 of 10 mm, an~. hole number 1 for Dry Creek, with a o50 . of

20 mm. Under these circumstan:2es,. ilnd considering that all four reaches receive their gravel from adjo'infng .areas which are likely to have similar lithology and weathering, I decid~d to assume that subpavement o50 is 20 rnm and 'l'oughness k = 212 mm for a 11 four reaches.

'.!. " •.

~"": t.:..· GEOMETRIC DATA SYNTHESIZED FROM HYDROLOGIC CONSIDERATIONS ' ~ l \ J ... ~.

. • . . ..• r

Equation 2 can be used ~o relate discharge to geometric parameters at flood stages in wide channels.

1· used t.his equaticjf to predict bankfull discharge Qb

using the previously determined values of k, Hb, Bb,

predicted va 1 ue of Qb 1 s 646 cumecs.

(3)

in Reach Z,

and S. The

In order to check this value, I back-calculated Qb fr~m ·each_ of

Equations la and 1b; the average of the two va 1 ues determined thus is 656 cumecs. In addition, an evaluation of the flood frequency of this discharge (out 1 i ned subsequently) indicated that a peak flow of 646 cumecs corresponds to a return period of 3.6 years. A typical value for Alberta streams that are incised is about five years; in more humid regions the value drops to about two years. Thus the estimated value of Qb for Reach 2, whether right or wrong, is ~t 1 east rea so nab l e.

·~

The hydrologic data include monthly flows for Poplar Creek near Dutch Gulch, (i.e., Reach 1) the South Fork., and Poplar Creek near Cottonwood. Also provided are flood frequency curves for PopJ~r. Creek near Dutch Gulch and Poplar Creek near Cottonwood. There are only four tributaries of con sequence from Qytch Gu1 ch to the gaging station at Cottonwood; they are in ordet· downstream: Dry Creek, Little Dry Creek, South Fork, and Hooker Ct .. eek. Thus I assumed the following hydrologic algorithm.

QDG + QDC + QLDC + QSF + QHC = QC

QDG = discharge in Poplar Creek at Dutch Gulch (Reach 1)

135

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Ooc = discharge from Ory Creek

QLDC = discharge from little Dry Creek

OsF = df scharge from South For'k

~~ = discharge from Hooker Creek

Oc = discharge fn Poplar Creek near Cottonwood

Insofar IS gravel-bed streams usually only n1ove gravel at flood stages, I concerned myself only with high flows. The flood frequency curves for natural conditions indicate that

QDG = 0.556 Oc (5)

at both the .two- and five-year floods. The monthly flows indicate that the river 1s highest for the months of January, February, and March. The average natural monthly flows for these three months obey the relations

QOG = 0.537 QC

OsF = 0.262 QC (6a)

(6b)

Note the good correspondence between Equations 5 and 6a. After some adjustment, I finally adopted the relations

for flood stages.

It 1s seen from Equations 4 and 7 that typically 17.3 percent of the flood discharge observed at Cottonwood must originate from Dry Creek, Little Dry Creek, and Hooke1· Creek. Any estimate for partition­ing flood flows among them based on the data provided to me must of necessity be very crude. I thus rowed with the oars I had. I measured basin areas Ace• ALoe• and AHC from the topographical map> provided; the map of normal annual precipitation allowed me to estimate annual pretfpftatfons Poe• PLoc• and PHc· The values are listed fn Table 2.

136

-

Table 2.. Annual pr~cipi~ati.on values;.

ANNUAL PRECIPITATION (mm)

Dry Creek. Little Dry Creek Ho.:,;ker Creek

71 154 83

740 700 600

Now 1 et roc = OociOc · be the: ratio of discharge from pr~ Creek· t~, ..

the discharge measured in Poplar Creek at high flows under natyral conditions: rLDC and rHC are ass~med to be.~imilarly defined. Note that from Equations 4 and 7,

..

roc + rLDC + rHC =. 0.173

I related the values of r to the ratios of annual volumes of water falling on each of the basins; to wit

and 1 i kewi se for rLDC and rHC.

The results of this computation are:

. Now since

is appropriate

and Ooc = Q4•

Goc = o.0433 Oc

QLDC = o.os87 Oc . , .

QHc = o.0410 Oc ,•

' ..

(9a)

.(9b)

(9c) .

the gaging station at Dutch Gulch is within Reach 1, it to define Ooc = 01. Likewise, one may defi n~ QLDC = Q3

From Equations 7 and 9, these definitions,

Q3 = 0.160 Q1

Q4 = 0.078 Q1

137

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(lOb)

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..... --By definition, the discharge in Reach 2, Q2, is gven by the algorithm

or thus Q2 = Q1 + Q3 + Q4

Q2 = 1.238 Ql (lOc)

Equations 10 are assumed to hold for high natural flows. They involve the very drastic assumption that the tributaries are always perfectly in phase with the main stem. The total basin for Poplar Creek is not large, and both annual rainfall patterns and the rainfall pattern for the storm of January 14-18, 1974 (assumed to be fairly typical) do not suggest the tributaries to be strongly out of phase with the main stem. Dry Creek and Little Dry Creek have considerably smaller basins than Poplar Creek upstream of Dutch Gulch, and so would normally be fl ashier. However, even this is mitigated by the fact that the upper reaches of the Poplar Creek basin typically receive much more rainfall than the two tributary basins; the lag time for infiltration in the typically drier tributary basins may counteract their flashiness.

'Now if bankfull discharge for Reach 2 is taken to be 646 cumecs, Equation lOc indicates a bankfull discharge for Reach 1 of 521 cumecs, assuming the sarne flood frequency for both. The flood frequency curve for Poplar Creek at Dutch Gulch indicates a return period of 3.6 years for this discharge, as was mentioned previously.

Extending the assumption of equal bankfull flood frequency to the tributaries, it follows from Equations lOa and lOb that Qb = 83.3 cumecs

for Reach 3 (Little Dry Creek) and 40.6 cumecs for Reach 4 (Dry Creek).

Data on bankfull hydraulic geometry must now be synthesized for Reaches 1, 3, and 4. Of Equations la and lb, the former has the higher coefficient of correlation; I decided to use it to estimate bankfull width Bb in Reaches 3 and 4, and then to estimate bankfull depth Hb

from the friction relation, Equation 3. The values thus obtained are Bb = 41 m and Hb = 1. 03 m for Reach 3, and Bb = 30.0 m and Hb = 0. 74 m for Reach 4.

A word of caution is in order about these va 1 ues. The em pi rica 1 width-discharge relation is one of the most consistent relations of river mechanics. Widths estimated from it can be expected to be fairly accurate in most cases if an accurate value of Qb is used. However,

herein Qb itself has been estimated for the tributaries in a very

approximate fashion. The subsequently presented gravel bedload calcula­tions are rather sensitive to variations in Bb, Hb, and Qb. In

addition, the 1:24000 topographical map of the Hooker, California quadrangle indicates that much of the valley of Reach 4 (Dry Creek) is filled with dredge tailings. It is possible that the stream channel itself is ill defined there.

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A value of Bb for Reach 1 can also be estimated from Equation la directly, but this would not recognize the fact that this reach is adjacent to another reach of the same stream for which Bb is known, i.e. Reach 2. It is thus useful to cast Equation 1a in the form

(11)

so that the previously determined value of Bb2

has a role in determining Bb1. Bankfull width for Reach 1 is thus found to be approximately 108 m. (If Equation 1a were used directly, the value

'would be fourteen percent smaller.) Bankfull depth can then be estimated from Equation 13 as 2.12 m.

The values of Bb and Hb for Reach 1 are lat~r adjusted slightly to facilitate gravel routing.

The measured and estimated bankfull parameters, and several others, for the four reaches under natural conditions are summarized in Table 3. L denotes the length of each reach, and BG denotes the typical width of mobi 1 e grave 1 on the bed during floods sufficient to mobi 1 i ze the bed. BG has been estimated as

( 12)

based on information on the cross sections and Parker (1979).

At this point, I questioned whether or not "bankfull" is even a va 1 i d concept for Reaches 1 to 4. Many grave 1 rivers are incised and have little or no genetic floodplain area. Both the cross sections and the topographic maps supplied indicate that Poplar Creek does have a floodplain in Reaches 1 and 2. The topographic map suggests that Little Dry Creek has a floodplain in most of Reach 3. The status of Dry Creek in Reach 4 is, however, open to question. Its valley seems to have been filled with dredge tailings. Whether this aggradational surface acts as a

11surrogate floodplain, 11 or whether the stream has incised into the

deposits, remains unclear.

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Table 3. Measured and estimated bankfull param~ters, and several others, under natural conditions.

REACH 1 REACH 2 REACH 3 REACH 4

Qb (m3/s) 521 646 83.3 40.6 Hb (m) 2.12* 2.25 1.03 0.74 Bb (m) 108* 119 41 30

BG (m) 87 96 30.7 22.6 s 0.00180 0.00186 0.00390 0.00569 o50 (mm) 20 20 20 20

k (mm) .212 212 212 212 L (mm) 8.26 6.23 6.13 4.57

*subject to later adjustment

NATURAL AND PROJECT FLOW DURATION CURVeS

The flow duration curves for both natural and project conditions at Dutch Gulch (Reach 1) were provided to me by the workshop organizers.

For a gravel routing scheme it is necessary only to consider flood flows high enough to break the pavement and mobilize the bed gravel. Parker and Klingeman (1980) have found a criterion due to Neill (1968) for bed motion in terms of pavement, namely

t = l ~~D ~ 0.03 p • p50

to take the approximate form in terms of subpavement

(13}

for many paved gravel-bed streams. (The implication is that DP 501050 is roughly 2.5.)

I used criterion (13), Equation 3, and an at-a-station relation for water surface width as a function of discharge in gravel-bed streams due to Parl\er and Peterson (1980) to estimate values of H and Q required for breaking the Ravement. The at-a-station relation is

140

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8 !L 0.16 8 = (Q )

b b (14)

The va 1 ue of Q so df!term1 ned for each reach was reduced to an equivalent discharge Qel in Reach l via Equation 10. A frequency of exceedance was then determined from the natural flow frequency curve at Dutch Gulch, and converted to a number of days per year for which each reach could be expected to have a mobile gravel bed. The results are given in Table 4.

Table 4. Conditions for bed gravel mobilization .

REACH 1 REACH 2 REACH 3 REACH 4

H (m) 1.36 1.32 0.63 0.43 Q (m3/s) 210 215 29.5 13.0

3 Qe1 (m /s) 210 174 184 167 days exceeded

per year 1.43 2.31 2.02 2.56

These values suggest that when applying the Dutch Gulch flow duration curve for natural conditions to gravel routing, flows less than 5912 cfs ( 142 cumecs) need not be considered. This corresponds to between a 1.1 and 1.2-year pe~k flood in Reach 1.

The portion of the Dutch Gulch flow duration curve relevant to gravel routing can then be converted to a histogram of discharge intervals 1 = 1, 2, 3, ... , typical discharge 01 (geometric mean) on each interval, and the fraction of time per year P; at which discharge falls in the interval. This is given for Dutch Gulch (Reach 1) for both natural and project conditions in Table 5: (Qi)N refers to natural values, and (Q1)P to project values in cumecs.

Thus, Table 5 constitutes the natural and project flow frequency relations for Reach 1. In accordance with the assumption that Reaches 1-4 are all perfectly in phase under natural conditions, the correspond­ing natural relations for Reaches 2, 3, and 4 can be obtained from Equation 1~ by multiplying (Q1)N by 1.238, 0.160, and 0.078, respec-tively. without altering the corresponding value of pi.

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Table 5~ Discharge intervals, typical discharge, and fraction of time per year discharge fall in that interval for natural and project conditions.

INTERVAL NO.

1 2 3 4 5 6 7 8

pi

0.0038 0.0028 0.0016 0.0009 0.0003 0.0001 0.0001 0,0001

159 200 252 318 400 503 634 798

141 192 244 277 307 328 339 350

The project flow frequency re 1 at ions for Reaches 3 and 4 can be taken to be approximately the same as the natural ones, as the only effects of a dam at Dutch Gulch on these tributaries would be backwater effects due to lowered baseline. The project relation for Reach 2 is rather more difficult to synthesize.

In the absence of any other guidelines, I made a sweeping assumption that I know is often erroneous. I assumed that the dam is operated only so as to chop off the peaks of flood flows more or less uniformly, the water thus stored being released at low flow or lost to evaporation or use. If this is the case, then the system of Reaches 1-4 are approximately in phase even under project conditions.

Before proceeding on this assumption, it may help to analyze how it might 1 ead to error. Suppose the dam is operated so as to comp 1 ete ly eliminate rather than just lower, say, spring snowmelt floods. In the spring flooding, Reaches 3 and 4 flow into a main stem that is not in flood. In this case, the tributary baseline is much lower than if flood peaks had simply been lowered. Tributary degradation and head-cutting should occur i.n either case, but these processes would be much ma.re severe when the main stem and tributaries are s·lgnificantly out of phase.

Proceeding ahead bo 1 dly or foo 1 ish ly as the case may be, perfect phasing under project conditions allows one to write

142

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rr·~·~ .. ~::.·~:~ . ;."~~-- i. it: .. , ~ .. .. • •

whee star jec· rep

WAT:

whe str.

~I . J J

~ v,n'!' +

J ~

where the subscripts 1, 2, 3, and 4 refer to Reaches 1-4, N and P stand for natural and project, and Equation 10 have been used. The pro­Ject flow frequency relation for Reach 2 fs then fou~d from Table 5 by replacing (Q1)N wfth (Q1)p) + 0.238 (Q1)N, but leaving p

1 unaltered.

WATER AND GRAVEL ROUTING FOR NATURAL CONDITIONS

The two basic tools for water and sediment routing rre a resistance relation and a sedfmen~ transport relation. Herein ~quation 3 is used for a resf stance relatfon. The selection of a sediment transport re 1 at ion , however, merits more care. Parker, K 1f ngeman, and Me Lean (1980) have determined an empirical relation for bedload in paved gravel-bed streams based solely on field data. The relation fs

W* = 0.0025 exp {14.2 (t-1) - 9.28 (t-1)2} (15a)

where W* fs a dimensionless bedload and t is a measure of ~latfve stress;

Rg W* = /9 (H:)3/2

* t -· 't --tr

In the above relations t* = HS/Ro50 is a Shields stl'ess based on subpdvement o50 , tr fs a referenc~ Shields stress equal to 0.0876 for field streams, q9 is volumetric bedload per unit wfdth of bed gravel, and R is submerged sediment specific gravity.

·Equation 15 fs shown fn Figure 4, along with ffeld data used to determine ft. Among the field streams listed on that figure, the Vedder River, British Columbia is quite similar to Poplar Creek. o

50 is about

19 mm, DpSO fs about 44 mm, Dpgo is about 90 mm, and the subpavement contains about sixteen percept sand. S is near 0.00195, although it is affected by backwater from the Fraser River to a certain extent, and the ranges of wfdth, depth, and discharge at which bedload has been measured are respectfvely, 85 - 90 m, 1.34 - 1.60 m, and 216 - 370 cumecs. In the context of computing "edload fn Poplar Cree~ and its tributaries, this lends a glimmer of nope to an otherwise futile task.

143

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0 0 0 0

e Oak Creek o Elbow River

o Snoke River DVeddar River

<>Alberto Experiments •SAFHL Experiments

Figure 4. Gravel transport relation.

144

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l -­l

~ I

y f m b c s i A ;

n t

I m '

. ~

fl ' t .. ~

If ~:~

In fact, Equation 15a is valid only for 0.95 < ~ < 1.65. For ; ~ 1.65, the extension

0.8~1 415 W* = 11.2 (1 - --~) (15bj

may be used. For ; < 0. 95 grave 1 1 oads are so small that W* can be set equal to zero in a calculation of annual gravel Yield.

It must be understood, however, that Equation 15 cannot predict tota 1 bed] oad in paved grave 1-bed streams. Imp 1 i cit in its i ncorpora-tion of onTy a subpavement median grain size to describe grain size distribution is the·assumption that the size distribution of the annual Yield of bedload is similar to that of the bed material. This is in fact the case in many gravel-bed streams. Other such streams, however, may transport considerable quantitie~ of sand as bedload over a gravel bed, so that the content of sand in the bedload far exceeds its bed content. The quantity of sand moving at any given time is a function of supply from outside sources. Thus sand moves through the stream without increasing sand content in the bed, and acts very much like wash load. As long as the bed material remains essentially a gravel matrix contain-ing not more than about 25% sand in its pores (i.e. not exceeding the porosity of the grave 1 matrix), this and "throughput" J oad p 1 ays on Jy a negligible role in the process of slow aggradation or degradation; th~s the use of Equation 15, which neglects it, is justified .

There is one case, however, where it would appear that throughput sand can be incorporated in large quantities in the bed, namely, rapid deltaic aggradation at, e.g., the mouth of a tributarY': The author has observed this in pilot laboratory experiments at the University of Alberta, and Milhous (1980) reports several field occurrences.

..

let MNi i = 1, 2, 3, 4 denote this mean annual Yield of gravel from Reaches 1 to 4, in metric tons, based on the natural flow frequency curve. Assuming that the stream system is in grade, it follows from the definitions in Figure 1 that

(16)

In fact, there are enough vagaries in a natural system and uncertainties in such simple equations as Equations 3 and 15 so that predictions based on them rarely satisfy Equation 16 exactly. However, a sediment routing that does not predict graded conditions when condi­tions actually are in grade can hardly be expected to predict stream response to imposed changes accurately. I resolved the problem by

145

-

:

~·~

~~

r I - J'. J t ! • ,E 1

r 1 i•

r -l r lc I r I 1 r

r !' 1 ., .. ! •

I f; l• l

't- 1

lj I l

1 lt ', : r

.

l I .

!;

~·~ ;. ~

r ! ' '

~~

H

Jj

J ! . '

f; L

I : L

L . rc·- .. ,.

11

zeroing11

the system~ Herein this is accomplished by making slight changes in bankfull width of one of the reaches until Equation 16 is satisfied.

The calculation of annual grave) yield is performed as follows. CoNsider the ith reach at the jth discharge range of its flow duration curve, i.e. at discharge O;j· Width at this discharge is calculated from Equation 14 and depth from Equation 3. The only exception is that for which Qij exceeds Qbi' the bankfull discharge. In this case, I

made the facile assumption of infinite floodplain storage, so that 11

effective~' depth and width are never allowed to exceed their bankfull values. Volumetric bedload per unit width of bed gravel (q

8)ij is

calculated from Equati.on 15. The total a~•1ual mass yield Mi is then obtained from an appropriate summation in j:

7 M; = 8.36 x 10 BGi !(q8) .. P. · j lJ lJ (17)

(The factor 3.15 x 107

converts seconds to years; a specific gravity of 2.65 is assumed for the gravel.)

Annual yields calculated in this fashion before zeroing are shown in Table 6. It is seen therein that

providing a measure of the deviation from Equation 16. Trial-and-error adjustment of the bankfull width of either Reach 1 or Reach 2 could be performed in order to en sure that the terms on the 1 eft-hand-side of Equation 16 equal zero. However, it was obvious to me that any adjust­ment should be done on Reach 1; the value of Bb for it was synthesized, whereas the value for Reach 2 was measured.

The results of such an adjustment for Reach 1 are Bb = 97 m and

Hb ~ 2.26 m (calculated via Equation 3); this amounts to a 10% reduction in bankfull width. The zeroed value of MNl is shown in Table 6.

146

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....

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,, ·- .. ,..·--·-·.~····•, --~·····~-; jl

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1: ltl

ff

r r

.,J! ,,

l~ ,, ' .

~\

~\ ' .

l J~ ! ~

"

\). ' -: ' . .)

Table 6. Annual yields calculated before and after zeroing.

REACH

1 before zeroing 1 after zeroing 2 3 4

MNi (metric tons/year)

107.2 206.2 372.3 75.2 92.9

Equation 16 is seen to be satisfied within one percent. The low yields of Tab 1 e 6 are, in my experience, not unusua 1 for grave 1-bed streams with self-formed gravel banks.

SHORT TERM WATER AND GRAVEL ROUTING FOR PROJECT CONDITIONS IGNORING TRIBUTARY DEGRADATION

Water depths and gravel yields may now similarly be calculated for project conditions using the flow duration curves developed in Section 5 and the zeroed values of Bb, Hb, and BG for Reach 1. Herein this is done under the hypothesis (later found to be wrong) that gravel yiel·ds as well as.water yields remain unaltered in the tributaries. That is, project yields Mp3 a~d Mp4 are assumed to equal, respectively, MN3 and MN4.

Project gravel yields are shown in Table 7.

REACH

1 2 3 4

Table 7 Project gravel yields.

Mp;

(metric tons/year)

26.5 104.9 75.2 92.9

Percent of Natural Value

13 51

100 100

The predicted values apply for the short term {first few years) .

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It is seen that the effect of the dam on Reach 1 is profound; annual gravel yield which was not large under natural conditions has been reduced to only a small fraction of that. Although a detailed calculation using the method of Parker and Kiingeman {1980) was not performed, the values of ~ associated with project conditions in Equation 15 are small enough to indicate that the gravel load consists mostly of the finer grains available in the pavement, so that the pavement coarsens into an armor~ and Reach 1 tends toward static equilibrium.

The coarsened surficial layer acts to protect the substrate from modification. Thus no immediate change in subpavement structure should occur. Indeed, the only long term modification likely to occur is the collection of fine material and organic debris from local sources in the substrate pores, as flows adequate to "fl ush11 the bed are not 1 ike ly to occur.

In Table 7, Reach 2 is also seen to have a lowered ability to move sediment under project conditions. The effect of the project is not so great due to the unaltered water supplies from the tributaries. On the other hand, the tri but aries are feeding in sediment at an unaltered rate. The result is deposition of sediment at the upstream end of Reach 2 as the main stem is unable to move the contributions from the tributaries. The deposition rate is

(18)

Initially this should occur as a deltaic deposit at the mouths of the tributaries. Later, it is shown that this value vastly underestimates the short term deposition in Reach 2. However, it is seen that gravel continues to move through Reach 2 fairly actively. Except in the immediate vicinity of deltaic deposits, where fines may be trapped, both gravel payment and subpavement should remain relatively unmodified in structure, implying a healthy substrate for fish .

Short term degradation and aggradation rates can be estimated by the equation of conservation of bed sediment, where p is bed porosity, z is bed elevation, t is time, and x is a down-channel parameter,

(19)

Cast in a discrete form appropriate for the present calculation, it takes the form

AZ = 1 (M M ) 1 (1-p)BGL IN - OUT 2.65 (20)

148

-

,

I I

I ' '

~

'I

where bz denotes the change in mean bed elevation on a reach in meters in ~ne year and MIN and MOUT are annual gravel transport rates into

and out of the reach in tons.

The computed va 1 ues of Az for Reaches 1 and 2 are exceedingly

sma 11, being -2.5 x 10-2 mm for the former and +8. 7 x 10-2 mm for the latter (the minus si'gn indicates degradation); a value of p of 0.35 has been assumed. Part of the reason for the smallness of the values may be the long extent of the reaches over which they are computed; i.e. the grid may be too coarse. However, even if the degradation rate in Reach 1 is actually one hundred times larger, the implication is unaltered; flows are reduced so much in this reach that it very quickly reaches a state hardly removed from static stability. The short term potential for degradation here is exceedingly small.

The small aggradation rate predicted in Reach 2 is, however, probably very erroneous. The source of the error is 1n the assumption Mp3 = MN3 and Mp4 = MN4 for the tributaries. Controlled dischar~e

releases from the dam imply lower water surface elevation in Reach 2 during floods. This implies an immediately lowered flood baseline for both of the tributaries as soon as the project is put into operation. The only way the tributaries can respond to this is by degrading their bed. Degradation should work its way upstream; gravel delivery rates to the main stem should temporarily (several years or more) incr~ase, and much more deposition should occur in Reach 2 than that indicated by Equation 18.

The lowered baseline is ill1ustrated in Figure 5 in terms of a probabi 1 i ty of exceedance of gi van depth va 1 ues (based on the flow duration curve) for natural and project conditions.

It is perhaps of value to nt\te that the qualitative predictions that I have made herein are in agreement with the field observations of Kellerhals and Gill (1973) on the Peace River and its tributaries down­stream of the W.A.C. Bennett Dam, British Columbia.

THE SHORT iERM EFFECT OF TRIBUTARY DEGRADATION

While it is not difficult to reach the conclusion that Dry Creek. and Little Dry Creek will be subject to degradation due to lowered baseline during flood, prediction of the degradation and the associated yields of gravel is a different matter.

I have attempted to obtain simple results by means of a crude numerical model aiong the following lines.

a. A "dominant discharge" Qd was evaluated for each tributary;

it is defined such that if continued constantly for the por­tion of the year for which f ~ 0.95 (i.e., gravel load is not vanishing), it would transport the natural annual gravel load. The fraction of the year for which f > 0. 95 is 0. 0031 for both tri but aries. A va 1 ue Qd = 59.7 cumecs was found for

149

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(

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,_)

"'1r, i .. : ""'· -=~ ~ ,. :> ' . .. . ' ' .

H(m) /Natural

lo-a Exc.!edance Probability

Figure 5. Depth exceedance curves, Reach 2.

150

1-l ' t

i

r;· [I

f

f

t."

{ . ,,

Reach 3, and 28.8 cumecs for Reach 4. These correspond to discharges ot 373 and 369 cumecs, respectively, in Reach 1 at the same exceedance probabi 1 i ty of the flow· duration curve, via Equation 10. A good average, then, is 371 cumecs on Reach 1, or via Equation 10, 459 cumecs on Reach 2. These discharges have an annual probability of exceedance of 0.000547, which is essentially id~ntical to that of the dominant discharges in the tributaries. The conc(~pt of a yield-defined dominant discharg~ is introduced so that a degradation calculation can be performed under steady flow conditions that are in some way equivalent to a typical yearly hydrograph.

b. The depth in Reach 2 with a natural probability of exceedance of 0.000547 (i.e., the depth at 459 cumecs) is 1.90 m. The depth with the same probabi 1 i ty of exceedance in the same reach under project conditions is 1.74 m (at a discharge of 386 cumecs). Thus a drop in baseline at 11 dominant11 conditions of 0.16 m is realized.

c. This drop is realized in the short term in terms of a drop in main stem water surface level at the tributary mouth. A proper calculation of degradation thus requires backwater curves at each step. To avoid this in a simple calculation, I replaced decreased water surface elevation at the mouth with a step on the bed consisting of an initial drop of 0.16 m spread over 20 m from the tributary mouth upstream. I then assumed that normal depth calculated from Equation 3 is realized everywhere and at all times in the tributaries.

d. Each tributary was assumed to have the constant bankfull geometries listed in Table 3 from mouth (except for the step) to a point 2500 m u_pstream which was assumed to be far enough upstream not to be affected by degradation in the short term. Initial bed profiles are shown in Figure 6a. "Dominant discharge" was then imposed continuously on each tributary, and degradation was calculated by means of a numerical solu­tion to Equation 19, with the aid of Equations 3, 14, and 15. One year of real time was assumed to pass for each period of 0.0031 years for which the numerical calculation was per­formed. Programming was done with the aid of the University of Alberta Amdahl computer.

The bed profiles of the tributaries before and after two years are shown in Figure 6b. It can be seen that 16 em is gradually working its way upstream, and that considerable potential for degradation remains after two years.

In Figure 7 the cumulative sediment yield from each tributary is plotted versus time. After one year Little Dry Creek is seen to put 2550 tons of gravel into Reach 2, and Dry Creek yields 1670 tons. These values are, respectively, 34 and 18 times the annual natural yields.

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n=:= '1'i:!.l ~ u- \.. ~-JSL.-

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L ---------------------- ----"'··-·· ; .

"'·'~ _,

~jl~·- J;;:_a ·-g ii ,...-.- ~

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100

""'-~

----- :·~- ~

Dry Creek

·-­-- -« ::I

. Assumed Initial Profile

Profile After Two Years

Distance Upstream of Confluence (m)

Figure 6b. Bed profiles after two years.

---- --·-·--- ----,-

r·~·-·"'51 ~. ~--r_. :-

0

. "-~-~---·r-. , ... .,..,...,..,¢__...,...t·~·-.~···· ..... ~~~· ............ ~,~-- ,... ....... .,.__...,..,...,.... . ._,._...._ __ .......

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n id

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CI)

Q) c E·--E ~ rooo >o Q)~

.:! -o .... Q) c .... -CD ~ > E= ~ CP. uo

Little Dry Creek~ .

'Dry Creek

Time In Years

Figure 7. Gravel supply from tributaries.

154

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io ! ! ~ . ~

Th armor ( impl ici; 1 i ne dr

';;

Ttl I

cond1tdi f infee ~ t the va t

s~ i repre ' I f Initia' r.

bui ldi1 f is the become tion ! . Reach :: 1

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makes • losin· ; from I ~ Equat~ : condi, unde~ bankf width Equat

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These values may represent overestimations in that any tendency to armor and stabilize 1 s not accounted for. On the other hand, the 1~p11cit assumption of perfect phasing tends to underestimate the base· line drop, and thus the degradation and sediment yields.

The aggradation rate for Reach 2 for the first year of project conditions can be computed from Equation 20 and these ne~ ·gravel infeeds. The calculated value of 4z is +4.0 mm/year, or about 46 times the value obtained by ignoring tributary degradation. However, this represents only an average aggradation rate over the ent 1 re re~~h. Initially this aggradation should take the form of large, rapidly· building bars localized downstream of the mouths of the tributaries. It is these bars that have the most potential to capture fines, and thus become unsuitable for spawning. Downstream of these bars, the aggrada­tion should be gradual, so that fines can be washed out; thus most of Reach 2 would likely remain suitable for spawning.

It should b~ noted that the tributary degradation calculations have been performed under the unverified assumption that no controls such as bedrock outcr(ps exist in the reaches under question.

LONG TERM CHANGES IN CHANNEL GEOMETRY

The long term modification of Poplar Creek as it attempts to find 1 new equilibrium can be surmised in terms of a stable Reach 1 and tributary degradation that has run its course.

Since flood discharges have been lowered in Reaches 1 and 2, ft makes sense to assume that the channel will respond by narrowing and losing capacity via vegetation growth and collection of fine material from local sources. This reduction in width can be estimated from Equation la if some kind of 11 surrogate11 bankfull d1 scharge for project conditions can be estimated. I did this by calculating discharges which under project conditions hav~ the same exceedance probability as bankfull discharge into a true bankfull dischar-;~. Before this happens, width at the 11 surrogate11 bankfull . di schat~i! ··can be estimated from Equation 14, yielding values of 90 m for Reach l and 112 m for Reach 2.

After the adjustment takes place, the eventual bankfull width can be estimated from Equation la cast in the form

where i denoteS... initial (preproject) and f denotes final val_ues. The va 1 ues so predicted are 79 m for Reach 1 and 102 m for Reach 2. Thus, a noticeable contraction in bankfull width is predicted. A

155

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' 1 i i

l i.

! ' t 1:

!

I ' (' r

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contraction of this order will likely occur in Reach 2 eventually, -as it will still be morphologically active in the long term. A contraction is a 1 so 1 ike ly to occur in Reach 1 due to debris deposits and vegetation encroachment. Whether it can be predicted accurately from Equation la, however, is problematic in that asymptotically the reach should be rendered morphologically dead. Indeed, if width maintenance is heavily dependent on the availability of fines for deposition, channel widening can actually occur downstream of a dam (Einstein 1972). However, this is not likely in the case of Poplar Creek, with its gravelly banks.

Reach 1 should reach stabi 1 i ty very s 1 owly by a combination of coarsening and degradation; channel narrowing should abet this process somewhat. Parker (e.g., 1980a) has observed degradation and transition from pavement to stable armor in the laboratory; preliminary results suggest that final armor median size mignt be about 1.3 times the natura 1 pavement DpSO, or about 65 mm. Assuming that armor o90 is twice the armor o50 and roughness height k is twice the armor o90 , and employing the Neill criterion for stability, Equation 3, and an assumed value of bankfull width of 79 m, a fina1 stable slope of 0.00153 can be calculated for Reach 1.

In treating Reach 2, I assumed that eventually tributary degradation would run its coarse, and annual tributary gravel yields would return to their natural values in Table 7. With no gravel contri­buted from the stab 1 e Reach 1, tt:en, Reach 2 must convey 168.1 m.~tri c tons per year through a channel with an estimated bankfull width of 102 m. A routing using the project flow histogram indicates that channe 1 slope must be equal to 0.00189 for this to happen, assuming no change in gravel composition.

The implication here is that the short term aggradation of Reach 2 wi 11 be fo 11 owed by a s 1 ow, 1 ong term degradation driven by a return. of tributary yi e 1 ds to their former va 1 ues and channel narrowing. The fi na 1 channe 1 of Reach 2 wi 11 st i 11 be active an£! fit for spawning. Unless corrective measures are taken to clear debris from Reach 1 by, for ex amp 1 e, the re 1 ease of appropriately high flows from the dam, it may eventually become unfit for spawning.

1 ~] MEANDERING AND THE POOL-AND-RIFFLE STRUCTURE

'

fl '= ( '

Kinoshita (1957) has classified free meander patterns according to their sinuousity. Low-sinuosity channels usually have two pools, bars, and riffles per bend wavelength; that is, meander bend wavelength corresponds with the wavelength of the pool-and-riffle pattern. Tortuous channels may have as many as six pools per bend.

Typical meandering gravel-bed streams, including Poplar Creek, are of 1 ow sinuosity. Where the meander pattern is free, then, coincidence of the meander pattern and the pool-and-riffle pattern may be assumed.

l I ----~1 r -

-

In; cannot t Reach 2.:· which 1; meander· sinuosi· ; n this

I Ander so, !.Parker '

;

I }

respec: Anders we 11 1, ,, : sinuo1..: Figure eters. Table

The ! side\ 1itt; obse,

\

I stre dam\ def~: yet\

I

in much of Reach 1, Poplar Creek impinges on a steep cliff, and .. cannot be said to be completely free. However, the upstream half of

Reach Z shows a well defined succession of five alternate bars about which the channel displays meandering of low sinuosity. Typical meandering gravel-bed streams, including Poplar Creek, are of low sinuosity. I determined an average linear meander wavelength of 1410 m in this portion.

I compared this value with the predictions from two formulas, the Anderson formula and the second form of the modified Anderson formula (.Parker and Anderson, 1976). They tal<.e the forms

(21a)

(21b)

respectively; lambda denotes wavelength, and a= 0.707 in the modified Anderson formula based on data. Both of these formulas appear to work well for both laboratory alternate bars and field bars and bends of low sinuousity. This is illustrated for the modified Anderson formula in Figure 8. I employed Equation 21 in conjunction with bankfull param­eters. Predicted wavelengths und~r natural conditions are summarized in Table 8; ~OBS denotes the observed value.

Table 8. Pre~Jcted ~avelengths under natural conditions.

~OBS (m} ).A (m)

~MA (m)

REACH 1

758 884

REACH 2

1410

844 97t

The va 1 ues predicted from either Equation 21a or 21b are on the sma 11 side in the case of Reach 2, but not reasonably so. Equation 2lb is a little better, predicting a value that is 31 percent lower than the observed va 1 ue.

I then used Equation 21 to predict meander wavelength to which the stream will tend for short term project conditions immediately after the

~~ dam is put in operation, using the 11 surrogateu bankfull discharges ~ defined prev1 ous ly and the assumpt 1 on that r :1anne 1 contract 1 on had not

yet occurred. In addition, a calculation was performed for the long

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Fisure 8. Relation for 11eander w·avelenatb.

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1

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101

Fiaure 8. Relation for Mander wavelensth.

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term channel geometry in Reach 2 after contraction has occurredw This was not done for Reach 1, as a 1 ong term state of zero mobi 1 i ty is incapable of determining its own meander pattern. Percent changes about the predicted values under natural conditions are also shown below in Table 9.

Table 9. Percent changes about the predicted values under normal natural conditions.

Reach 1 short-term Reach 2 short-term Reach 2 long-term

637 739 729

Percent Reduction

16 12 14

726 843 830

Percent Reduction

18 14 15

The results indicate that both Reaches 1 and 2 will initially begin to reduce their meander lengths. The process is unlil<.el.Y to be very effective in the case· of Reach 1 due to the near-vanishing transport

·rate and the control exerted by the cliffs on the south bank. Reach 2 should be able to maintain, in its final state, a meander pattern that is perhaps fifteen percent shorter in wavelength than that observed presently.

The adjustment in Reach 2 should take at least five to ten years, and would likely be disrupted at the upstream end by bars building out from the tributaries. However, the amount of adjustment is not large enough to suggest massive instabilities throughout the entire reach during adjustment.

SUMMARY OF PREDICTIONS FOR 11 POPLAR11 CREEK AND ITS TRIBUTARIES.

The reach of Pop 1 ar Creek from the dam to just upstream of Dry Creek (Reach 1) will be almost immediately rendered incapable of moving much gravel by the project. It has negligible water and gravel infeed from tributaries. The gravel that moves is likely to be on the fine side. The low transport rates of gravel (gradually declining from about one tenth of the natural rate) imply extremely slow degradation, with a gradual coarsening of the pavement. After a very long time the bed slope might decrease by a maximum of fifteen percent, accompanied by perhaps a thirty percent coarsening of the surficial material. The maximum potentia 1 for degradation is rough 1y two meters for the reach, but it may take hundreds of years to realize this, and it may never be realized at all if the width in the reach does not contract.

159

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A conventional formula for hydraulic geometry of active gravel streams suggests that if the reach is able to contract and form a new, smaller bankfull channel, bankfull width.would be reduced by roughly twenty percent. Some reduction in width can be expected even for this essentia1ly inactive channel (after control) due to vegetation encroachment.

The near-vanishing transport rates also suggest that the substrate will be locked into place. It will suffer only very minor modification due to bedload transport, as most of the coarsening will occur on the surface. However, locally derived fine sand, silt, clay, and organic debris will likely collect in the substrate in increasing quantities under the proposed project flow duration curve, as no mechani srn would exist to clean it. ·

Some cementing of the substrate is also possible. These effects could be avoided or mitigated by modifying the dam operation to allow for occasional short, large releases.

In any event, these processes which act to degrade the substrate of Reach 1 are slow, so that if it is prese~tly suitable for spawning, it should remain so for at least the first few years after commencement of dam operation.

The reach of Pop 1 ar Creek from just upstream of Dry Creek to a point upstream of the confluence with the South Fork (Reach 2) presents a different situation. Lowered project discharges should roughly have the capacity of this reach to move gravel. The implied lowered baseline due to flow control should also induce degradation in Dry and Little Dry Creeks, with consequent rapid deltaic deposition at the upstream end of the reachs and initial slower aggradation of the reach as a whole.

Computed gravel infeed rates from the tributaries as they degrade for the first year or two are on the order of 25 times their natural f·eed rates. The resulting local bars at the upstream end of the reach may thus initially incorporate considerable sand (if it is available) and have substrates unsuitable for spawning. As the aggradation slowly spreads over the entire reach, it is likely that excess fines would be washed out. Most of the reach should maintain a substrate suitble for spawning during this process.

On the order of 10 to 15 em of degradation should work its way up the tributaries. The amount will be more if tributaries and main stem are far out of phase under project conditions. The tributaries may respond by initially coarsening their bed sut"faces; if they are used for spawning this may have a deleterious effect.

In the long .term tributary degradation will eventually run its course. Tributary bed structure, gravel load, and gravel content are likely to gradually return to values typical of preproject conditions.

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Thus, fn the long term the main stem in Reach 2, which was initially oversteepened by transient high tributary gravel inputs, should slowly degrade back to a situation where it can transport near­

·natural (previous to the project) gravel inputs from the tributaries, with no input of gravel from the main stem upstream.

At the same time as this degradation occurs, the main stem channel should narrow to adjust for the r'educed flood flows. I estimate this narrowing to be in the neighborhood of 15%. I al~n estimate that after th i s reach goes thr·ough its eye 1 e of short term aggradation and 1 ong term degradation, it will reach a graded'slope very nearly equal to the present value.

Both short term and long term tendencies indicate a reductinn in meander wave 1 ength by about 15%. This wou 1 d p robab 1 y be accomp 1i shed slowly, Without an excess of dfsruption of the channel except at the upstream end of Reach 2 in the deltaic deposits. Here, severe local channel instability may occur.

In brief, Reach l should be healthy for spawning in the short term, but should eventually become morphologically dead, with deleterious effects on spawning. Reach 2 should undergo rather severe aggradation, with possible incorporation of fines, at the upstream end fn the short term, The rest of the reach should not be too unstable in the short term. The long term prognosfs 1s for a narrower, smaller, but still active Reach 2, that is otherwise not much different from natural con­ditions, and in that sense, morphologically and biologically healthy.

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REFERENCES

Einstein, H. A. 1972. In: River Ecology and Man (ed. R. Oglesby), pp. 309-318, Academic Press.

Ke11erhals, R., and D. Gill. 1973. Proceedings, 11th Congress, Int. Comm. on Large Dams, Madrid.

Kinoshita, R. 1957. Proceedings, Japan Society of Civil Engrs., No. 42.

Milhous, R. T. 1980. Proceedings, Intl. Workshop on Engineering Problems of Gravel-Bed Rivers, Wales.

Parker, G., and A. G~ Anderson. 1976. Proceedings, ASCE M~deling, 175 Conf., San Francisco.

Parker, G. 1979. Journal of the Hydraulics Division, ASCE, Vol. 105, No. ~~Y9.

Parker, G .• 1980a. Experiments on the Formation of Mobile Pavement and Static Armor, Report, Department of Civil Engineering, University of Alberta .

. Parker, G. 1980b. Discussion on Regime Relations for Gravel-Bed

Streams, Proceedings, Int 1. Workshop on Engineering Prob 1 ems of Gravel-Bed Rivers, Wales.

Parker, G., and A. W. Peterson. 1980. Journa 1 of the Hydrau1i c:s Division, ASCE, Vol. 106, No. HYlO.

Parker, G., P. Klingeman, and D. McLean. 1980. Bedload in Natural Paved Gravel-Bed Streams. Submitted to ASCE Hydraulics Division.

Parker, G.s and P. Klingeman. 1980. Bedload Size Distribution in Paved Gravel-Bed Streams. Submitted to ASCE Hydraulics Division.

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